Constructing relations in the Torelli group

Abstract: The mapping class group is the group of all orientation-preserving self-homeomorphisms of a surface (up to isotopy). Mapping classes define a natural action on the first homology of the surface; this gives us a representation from the mapping class group into the integral symplectic group. The kernel of this representation, the Torelli group, is the rich and mysterious subgroup of the mapping class group whose action on the first homology is trivial; although a classical object, its algebraic structure of the Torelli group is not yet completely understood. We construct some new relations in the Torelli group using surface braid groups based on work by Birman, Johnson and Putman.

Mathematics

Audience: researchers in the topic

ANTLR seminar

Series comments: This is the Algebra, Number Theory, Logic and Representation theory seminar.